Design by Contract Framework for Quantum Software

To realize reliable quantum software, techniques to automatically ensure the quantum software's correctness have recently been investigated. However, they primarily focus on fixed quantum circuits rather than the procedure of building quantum circuits. Despite being a common approach, the correctness of building circuits using different parameters following the same procedure is not guaranteed. To this end, we propose a design-by-contract framework for quantum software. Our framework provides a python-embedded language to write assertions on the input and output states of all quantum circuits built by certain procedures. Additionally, it provides a method to write assertions about the statistical processing of measurement results to ensure the procedure's correctness for obtaining the final result. These assertions are automatically checked using a quantum computer simulator. For evaluation, we implemented our framework and wrote assertions for some widely used quantum algorithms. Consequently, we found that our framework has sufficient expressive power to verify the whole procedure of quantum software

A Fast Decision Procedure For Uniqueness of Normal Forms w.r.t. Conversion of Shallow Term Rewriting Systems

Uniqueness of normal forms w.r.t. conversion (UNC) of term rewriting systems (TRSs) guarantees that there are no distinct convertible normal forms. It was recently shown that the UNC property of TRSs is decidable for shallow TRSs (Radcliffe et al., 2010). The existing procedure mainly consists of testing whether there exists a counterexample in a finite set of candidates; however, the procedure suffers a bottleneck of having a sheer number of such candidates. In this paper, we propose a new procedure which consists of checking a smaller number of such candidates and enumerating such candidates more efficiently. Correctness of the proposed procedure is proved and its complexity is analyzed. Furthermore, these two procedures have been implemented and it is experimentally confirmed that the proposed procedure runs much faster than the existing procedure

Subaru Hyper Suprime-Cam Survey for An Optical Counterpart of GW170817

We perform a $z$-band survey for an optical counterpart of a binary neutron star coalescence GW170817 with Subaru/Hyper Suprime-Cam. Our untargeted transient search covers $23.6$ deg$^2$ corresponding to the $56.6\%$ credible region of GW170817 and reaches the $50\%$ completeness magnitude of $20.6$ mag on average. As a result, we find 60 candidates of extragalactic transients, including J-GEM17btc (a.k.a. SSS17a/DLT17ck). While J-GEM17btc is associated with NGC 4993 that is firmly located inside the 3D skymap of GW170817, the other 59 candidates do not have distance information in the GLADE v2 catalog or NASA/IPAC Extragalactic Database (NED). Among 59 candidates, 58 are located at the center of extended objects in the Pan-STARRS1 catalog, while one candidate has an offset. We present location, $z$-band apparent magnitude, and time variability of the candidates and evaluate the probabilities that they are located inside of the 3D skymap of GW170817. The probability for J-GEM17btc is $64\%$ being much higher than those for the other 59 candidates ($9.3\times10^{-3}-2.1\times10^{-1}\%$). Furthermore, the possibility, that at least one of the other 59 candidates is located within the 3D skymap, is only $3.2\%$. Therefore, we conclude that J-GEM17btc is the most-likely and distinguished candidate as the optical counterpart of GW170817.Comment: 14 pages, 9 figures. Accepted for publication in PASJ (Publications of the Astronomical Society of Japan

Age-Dependent Association Between Modifiable Risk Factors and Incident Cardiovascular Disease

BACKGROUND: There have been limited data examining the age-dependent relationship of wide-range risk factors with the incidence of each subtype of cardiovascular disease (CVD) event. We assessed age-related associations between modifiable risk factors and the incidence of CVD. METHODS AND RESULTS: We analyzed 3 027 839 participants without a CVD history enrolled in the JMDC Claims Database (mean age, 44.8±11.0 years; 57.6% men). Each participant was categorized as aged 20 to 49 years (n=2 008 559), 50 to 59 years (n=712 273), and 60 to 75 years (n=307 007). Using Cox proportional hazards models and the relative risk reduction, we identified associations between risk factors and incident CVD, consisting of myocardial infarction, angina pectoris, stroke, and heart failure (HF). We assessed whether the association of risk factors for developing CVD would be modified by age cat-egory. Over a mean follow-up of 1133 days, 6315 myocardial infarction, 56 447 angina pectoris, 28 079 stroke, and 56 369 HF events were recorded. The incidence of myocardial infarction, angina pectoris, stroke, and HF increased with age category. Hazard ratios of obesity, hypertension, and diabetes in the multivariable Cox regression analyses for myocardial infarction, angina pectoris, stroke, and HF decreased with age category. The relative risk reduction of obesity, hypertension, and diabetes for CVD events decreased with age category. For example, the relative risk reduction of hypertension for HF decreased from 59.2% in participants aged 20 to 49 years to 38.1% in those aged 60 to 75 years. CONCLUSIONS: The contribution of modifiable risk factor to the development of CVD is greater in younger compared with older individuals. Preventive efforts for risk factor modification may be more effective in younger people.</p